The relational network model grew out of an attempt to understand
a person's linguistic system as one that is able to operate 
for speaking and for understanding. The newcomer
to linguistics might suppose that such concerns are
shared by all those who try to construct theories of
language, since after all the linguistic systems of our minds are able to
operate. But the fact is that the majority of linguists just try to
analyze and describe various properties of texts, without a concern
for how our systems work in speaking and understanding.
(See analytical linguistics.)

Relational network theory began its development
without any formal notation and allowed notation to develop as
the analysis unfolded. The result was a network notation  not
as a design feature present from the outset but as the conclusion of
the process of analysis.

This network model is justified and was arrived at by analyzing
relationships among linguistic units. Starting with the
traditional assumption that a lexical item (likewise morpheme,
phoneme) is a unit of some kind, an object or symbol or combination
of symbols, we analyze its relationships to other units to which it
is related. For example, morphemes are somehow related to elements of
phonological expression on the one hand and to elements of conceptual
information on the other. They are usually represented as
symbols  for example, 'boy', and these symbols represent
their phonological (or graphic)
realizations. Obviously, they are therefore related to the elements of
their phonological realization and have to access them for production of
speech. These relationships can be represented
as connections, the minimum requirement for any kind of relationship.
Of course, positing
connections leads inevitably to the need to posit nodes  the
points connected. A morpheme also 'has' higher-level properties
 grammatical and lexical or semantic  and if we ponder
what the meaning of 'has' is here, it is that the morpheme is
connected to such properties. So we have further connections. But
after the relationships of the morpheme to other elements
 phonological, grammatical, etc. are thus plotted,
the symbol that has been representing it can be removed from the
resulting diagrams with no
loss of information. Whatever information it can be
considered to represent is now already represented in the depiction
of its relationships (Lamb 1999: Chapter 4). This is especially clear
in the case of the morpheme, since the symbol was just representing the
components
of its phonogical representation, but these are now directly represented
by connections. Similarly, what do phonological symbols represent? They
are just abbreviated notations for type and manner of articulation; so
they have connections to those phonological properties, and after such
connections are plotted, these symbols too are superfluous. A similar line
of reasoning applies to all the other linguistic units for which symbols
have been used. They turn out to be just abbreviations for sets of
connections.

Following this procedure, every unit of phonology and lexicon can be
seen to be what
it is by virtue of what its relationships are, and so can be
seen as just the point in the system which has those relationships. And it
appears that semantic and conceptual relationships can likewise be
handled as relationships, with no units (Pathways of the Brain,
Chapter 9).

Upon removal of
the symbols from the structure, the result is a network of relationships
 not symbols and relationships, just relationships, represented
as interconnections among nodes. For what do the usual
symbols for morphemes, for example boy, consist of? They are
(spoken or written) expressions. But in the network representation
the actual expression is already provided by the downward connections
to elements of the phonological system, so there is no need to have a
symbol within the system in addition.

In any case, the presence of symbols within the system would raise
a serious problem: Just how is the symbol to be detected by the
system, or distinguished from other symbols? After all, the brain
does not have little internal eyes to read symbols.

Thus the linguistic system, understood as a network, does not
contain symbols but is a system which interprets and
produces symbols  spoken or written. Symbols are
inputs and outputs of the system; they are not inside
it. If they were inside, the system would need a little symbol
interpreter in there to interpret them, as well as a symbol producer,
to write them. That is, somewhere within the brain there has to be
a system capable of interpreting and producing symbols which does
not contain symbols. Well, then, why not let this system be the
linguistic system itself? What use has it of internal symbols?

A pathway in the network from the auditory or visual perception of
a spoken or written word to the set of concepts or images which
embody its meaning within the cognitive system is precisely what
provides the system with its means of interpreting symbols presented
to it from the outside.

Traveling Activation
The network operates for producing or understanding speech by means of
activation traveling along its pathways. (Examples.)

Compact and Narrow Notation Relational networks of the form usually seen
in the literature are drawn at a relatively abstract level. They are like
highway maps drawn to a large scale. In keeping with their aim of
accounting for linguistic data, they leave out considerable detail that is
of interest for other purposes. But their lines are really two-way lines,
able to carry activation in two directions. But underlying this notation
is a model which does not have two-way lines. Rather, each line of the
ordinary (or COMPACT or CONDENSED) notation is considered to represent (in
the typical case) a pair of oppositely directed lines of the actual model,
as may be shown directly using the EXPANDED(a.k.a.NARROW) RELATIONAL
NETWORK NOTATION. Similarly, a node of the condensed notation
generally corresponds to two or more nodes of expanded notation (Lamb
1999: Chapter 5). (Illustrations). The "ordered AND" node of condensed
notation is more complex, as it has to provide not only for a combination
but also for the sequencing of the components.

For phonology, there are evidently two distinct (but of course
interconnected) subsystems, one for production, the other for
recognition, each made up of one-way lines and nodes. Lexical
structure, on the other hand, may achieve bidirectionality without
separate subsystems, by having both feed-forward and feed-backward
output connections from their nodes (Lamb 1999:Chapter 8). The model
has this property also in the conceptual and perceptual systems and
is in general agreement with Antonio Damasio's hypothesis of
representation of information in neural networks (Damasio 1989a,
1989b, 1989c).

Also, in the actual networks of the theory, connections differ in
strength. Similarly, the activation received by a node has a
continuous range of values, and the node responds according to a
sigmoid threshold function such that greater input results in a
higher degree of outgoing activation. A line of a given strength may
therefore carry varying degrees of activation.